So you're trying to connect to and screen share with a Microsoft Windows system? Try using CoRD, and see if you get any further.
With Mac, it's common to use Messages and Screen Sharing, but the Remote Desktop stuff usually means a VPN into the remote system and some other details. There are some previous similar discussions here and here — which will give you some background and ideas on the general issues with remote access, dynamic DNS and networking, though you'll have to deal with the Windows sharing separately.
As an alternative approach, a migration to an iPad can sometimes help folks that are having trouble with the complexity of a Mac OS X or Microsoft Windows system, too. That won't eliminate the problems and it'll be a different UI to learn, but it can be simpler.
Apple Remote Desktop is a product sold by Apple, and I'd guess that's probably not what you're using here. If you're having issues with Microsoft Remote Desktop package, please check with the Microsoft folks for assistance with that — I'm certainly not going to be any good at providing help with Windows itself, either.